关于树的二分优美标号  

On bipartite graceful labellings of trees

作　　者：姚明[1] 姚兵[2] 杨思华[2] 

机构地区：[1]兰州石化职业技术学院信息处理与控制工程系,兰州730060 [2]西北师范大学数学与统计学院,兰州730070

出　　处：《兰州大学学报（自然科学版）》2014年第6期875-880,共6页Journal of Lanzhou University(Natural Sciences)

基　　金：国家自然科学基金项目(61363060;61163054;61163037);甘肃省高等学校研究生导师科研项目(1216-01);甘肃省财政厅专项资金项目(2014-63)

摘　　要：已知树的二分优美标号可以得到一些逼近优美树猜想的结果.给出了树的二分优美标号定义,发现了一类非二分优美树,得到了一些构造大型二分优美树的方法.定义了树的k-二分优美,并且对自然数k p2-1证明了任何顶点的优美树都是k-二分优美的.The bipartite labelling of trees was used to produce results that can be regarded as an approximation toward the Graceful Tree Conjecture. The bipartitely graceful labelling of a tree was defined, a class of trees was found to be not bipartitely graceful, and some ways were presented for constructing a large scale of bipartite graceful trees. We defined a k-bipartitely graceful labelling of a tree, and showed that any graceful tree T on p vertices is k-bipartitely graceful with k ≤p/2 -1.

关 键 词：优美标号 二分优美 对偶标号 优美树猜想 

分 类 号：O157.5[理学—数学]